Question

A cubical solid aluminium (bulk modulus $=-V \frac{d P}{d V}=70 \,GPa$ ) block has an edge length of $1\, m$ on the surface of the earth. It is kept on the floor of a $5\, km$ deep ocean. Taking the average density of water and the acceleration due to gravity to be $10^{3} kg \,m ^{-3}$ and $10 \,ms ^{-2}$, respectively, the change in the edge length of the block in $mm$ is ______.

Answer 1

$B =- V \frac{ dP }{ dV }$
$70 \times 10^{9}=\frac{(1)^{3} \times 5 \times 10^{3} \times 10}{\Delta V }$
$\Rightarrow \Delta V=\frac{5}{7} \times 10^{-3}$
$\Rightarrow \frac{\Delta V}{V}=\frac{3 \Delta \ell}{\ell}$
$\Rightarrow \Delta \ell=\frac{5}{21}=0.238 \,mm$